Non-linear Redshift-Space Power Spectra

TL;DR

This paper derives the full non-linear redshift-space power spectrum for Gaussian fields, revealing complex angular structures and scale-dependent effects crucial for interpreting high-redshift cosmological observations.

Contribution

It provides the first comprehensive calculation of the non-linear redshift-space power spectrum including angular correlations, extending linear theory to more accurately model observations.

Findings

Coupling boosts small-scale power in the non-linear regime.

Large-scale power is slightly suppressed by small-scale velocity perturbations.

Non-linear spectra exhibit more complex angular structures than linear theory.

Abstract

Distances in cosmology are usually inferred from observed redshifts - an estimate that is dependent on the local peculiar motion - giving a distorted view of the three dimensional structure and affecting basic observables such as the correlation function and power spectrum. We calculate the full non-linear redshift-space power spectrum for Gaussian fields, giving results for both the standard flat sky approximation and the directly-observable angular correlation function and angular power spectrum. Coupling between large and small scale modes boosts the power on small scales when the perturbations are small. On larger scales power is slightly suppressed by the velocities perturbations on smaller scales. The analysis is general, but we comment specifically on the implications for future high-redshift observations, and show that the non-linear spectrum has significantly more complicated angular structure than in linear theory. We comment on the implications for using the angular structure to separate cosmological and astrophysical components of 21 cm observations.